Related papers: Uniform convergent scheme for strongly anisotropic…
In magnetized plasma, the magnetic field confines the particles around the field lines. The anisotropy intensity in the viscosity and heat conduction may reach the order of $10^{12}$. When the boundary conditions are periodic or Neumann,…
This paper deals with the numerical study of a strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. Furthermore, the recently proposed Asymptotic-Preserving…
The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet \& Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vlasov equation with a strong external magnetic field. In this…
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic…
We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following [Du Toit et al., Comp. Phys.…
Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an…
We initiate a study of anisotropic plasma at strong coupling using the AdS/CFT correspondence. We construct an exact dual geometry which represents a static uniform but anisotropic system and find, that although it is singular, it allows…
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation with a strong inhomogeneous magnetic…
This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in…
Strongly magnetized plasmas, characterized by having a gyrofrequency larger than the plasma frequency ($\beta = \omega_c/\omega_p \gg 1$), are known to exhibit novel transport properties. Previous works studying pure electron plasmas have…
The aim of this work is to introduce a numerical method to cope with the multiscale nature of confined plasma physics. These investigations are focused on fluid plasma description under large magnetic field. The difficulties in this context…
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
A magnetic field was recently shown to enhance field-parallel heat conduction in a strongly correlated plasma whereas cross-field conduction is reduced. Here we show that in such plasmas, the magnetic field has the additional effect of…
Particle acceleration and pitch-angle anisotropy resulting from magnetic reconnection are investigated in highly magnetized ion-electron plasmas. By means of fully kinetic particle-in-cell simulations, we demonstrate that magnetic…
Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the…
For static reductions of isotropic and anisotropic Magnetohydrodynamics plasma equilibrium models, a complete classification of admitted point symmetries and conservation laws up to first order is presented. It is shown that the symmetry…
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of…